Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 1, pp. 166--186

PARAMETRIC AND SEMI-PARAMETRIC ESTIMATION OF REGRESSION MODELS FITTED TO SURVEY DATA

By

DANNY PFEFFERMANN and MICHAIL SVERCHKOV
* Hebrew University, Jerusalem*

*SUMMARY.* This paper proposes two new classes of estimators for regression models
fitted to survey data. The proposed
estimators account for the effect of nonignorable sampling schemes
which are known to bias standard estimators. Both classes derive from relationships
between the population distribution
and the sample distribution of
the sample measurements. The first class consists of parametric estimators.
These are obtained by extracting the sample distribution as a function of the population
distribution and the sample selection probabilities and applying maximum
likelihood theory to this distribution. The second class consists of
semi-parametric
estimators, obtained by utilizing existing relationships between moments
of the two
distributions. New tests for sampling ignorability
based on these relationships are developed. The proposed estimators
and other estimators in common use are applied to real data
and further compared in a simulation study. The simulations enable
also to study the performance of the sampling ignorability tests and
bootstrap
variance estimators.

*AMS (1991) subject classification.* 62D05, 62F10

*Key words and phrases. *
Bootstrap, nonignorable sampling,
probability weighted estimators, randomization distribution, sample distribution.